July 2017 DESCRIBED PROFICIENCY - SCALE FOR THE LITERACY AND NUMERACY TEST FOR INITIAL TEACHER EDUCATION STUDENTS
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DESCRIBED PROFICIENCY
SCALE FOR THE LITERACY AND
NUMERACY TEST FOR INITIAL TEACHER
EDUCATION STUDENTS
July 2017
Australian Council for Educational Research
Described Proficiency Scale for the Literacy and Numeracy Test
for Initial Teacher Education Students
This paper outlines the skills assessed by the national Literacy and Numeracy Test for
Initial Teacher Education Students (‘the test’) and how candidates’ achievement of the
standard required by the test is determined. The paper also describes the level of
proficiency of candidates and whether they are clearly above; at and above; or below
the test standard.
Background to the test
The test assesses aspects of the personal literacy and numeracy proficiency of initial
teacher education students.
All students undertaking initial teacher education programs in Australia are expected
to sit the test and demonstrate they have personal literacy and numeracy skills in the
top 30 per cent of the Australian adult population (‘the test standard’) prior to
graduating from their program. This requirement is described in the national program
standards: the Accreditation of Initial Teacher Education Programs in Australia,
Standards and Procedures, December 2015. The relevant standard is Standard 3.5.
Standard 3.5 Entrants to initial teacher education will possess levels of personal
literacy and numeracy broadly equivalent to the top 30% of the population.
Providers who select students who do not meet this requirement must establish
satisfactory arrangements to ensure that these students are supported to achieve the
required standard before graduation. The National Literacy and Numeracy Test is
the means for demonstrating that all students have met the standard.
The test standards (benchmarks) for literacy and numeracy were set with reference to
the judgement of groups of literacy and numeracy experts comprising teacher
educators, members of teacher regulatory boards, school leaders and assessment
professionals; and to the literacy and numeracy results for Australian adults from the
Organisation for Economic Co-operation and Development’s Programme for
International Assessment of Adult Competencies (2011–12).
Reporting candidate achievement
As part of their statement of test results, candidates receive advice as to which of three
bands their test score falls within for each test component (literacy and numeracy).
The three bands are:
• Band 3: Clearly above the test standard
• Band 2: At and above the test standard
• Band 1: Below the test standard
A small number of candidates may achieve scores above Band 3 or below Band 1. It
is not possible to describe these regions on the scale because there are insufficient
questions at these levels on the test. Descriptions of Bands 1, 2 and 3 are provided in
the tables that follow. The band achieved, together with any bands below it, shows
candidates the kinds of personal literacy or numeracy skills and knowledge they are
currently demonstrating. Where appropriate, candidates can refer to the statement in
1
the band above their test score to inform them of the skills that are required to reach a
higher standard of personal literacy or numeracy.
Candidates who have not achieved Band 2 should also seek support from their higher
education provider before re-sitting the test. The test administrator, the Australian
Council for Educational Research, issues providers with candidates’ achievement in
the sub-domains of each test component (literacy and numeracy) which assists
providers to offer appropriate support to improve candidates’ skills in the applicable
sub-domain(s).
The skills, knowledge and understanding demonstrated by candidates in each of the
three bands are provided on pages 3–13 for literacy and pages 14–36 for numeracy.
Sample literacy and numeracy questions for each band are included for illustrative
purposes.
2
Described proficiency bands for literacy
The following descriptions reflect the main content and processes assessed in the literacy component of the test. For literacy, the content
elements are reading and technical skills of writing (syntax, grammar and punctuation, spelling, word usage and text organisation). The process
elements of reading are access and identify, integrate and interpret, and evaluate and reflect.
Table 1: Band descriptions for Reading
Reading Band 1: Below the test standard Band 2: At and above the test standard Band 3: Clearly above the test standard
Candidates can typically Candidates can typically Candidates can typically
• locate directly stated information in a range • demonstrate the skills described in Band 1 • demonstrate the skills described in Band 1
of forms of writing, including factual, • make connections between information and Band 2
persuasive and narrative texts, and texts from different parts of texts that take a • synthesise, evaluate information from
with combinations of written material and variety of forms multiple parts of texts that take a variety of
images, graphs or tables • apply this information in making forms, including academic texts employing
• identify attitudes and opinions clearly interpretations high-level vocabulary
expressed in the texts • infer the position adopted by the writer of • interpret the effect of language in
the text communicating ideas and feelings
• evaluate the strategy adopted by the writer
Skills required to transition from Band 1 to Band 2 of a text
• evaluate the significance of textual
• make connections between information in texts elements (e.g. a quotation within an
• interpret information and the writer’s position in texts academic text)
• negotiate more sophisticated contexts and more subtle purposes in texts
Skills required to transition from Band 2 to Band 3
• evaluate information, positions and strategies
• interpret the effect of language and other textual elements
3
Table 2: Band descriptions for Technical Skills of Writing
Technical skills Band 1: Below the test standard Band 2: At and above the test standard Band 3: Clearly above the test standard
of writing
Candidates can typically Candidates can typically Candidates can typically
• identify written language use that is clearly • demonstrate the skills described in Band 1 • demonstrate the skills described in Band 1
inappropriate to a situation and purpose • select appropriate over inappropriate and Band 2
• correctly spell and use some words that are written language for a situation and • identify synonyms for high-level words
frequently misspelt, including homophones purpose • correctly spell some difficult polysyllabic
(e.g. new and knew) • correctly spell some polysyllabic words words
• recognise and apply aspects of punctuation (words with several syllables), including • correctly use less common punctuation
(e.g. in direct speech) some that are frequently misspelt marks (e.g. semi-colons)
• extend plans for writing (e.g. accurately • recognise and apply aspects of • critique and improve upon an existing
place a new idea into an existing structure punctuation that are frequently misused structure of ideas in a plan for writing
of ideas) (e.g. apostrophes)
• revise plans for writing (e.g. identify
whether and how a new idea fits into an
existing structure of ideas)
• Skills required to transition from Band 1 to Band 2
• correctly spell more difficult words
• correctly use more commonly misused punctuation
• have greater understanding of how to express ideas in a piece of writing and how they
should be structured
Skills required to transition from Band 2 to Band 3
• know the meaning and spelling of more difficult words
• correctly use less common punctuation
• structure writing in a sophisticated way
4
Sample questions illustrating the literacy band descriptions
Band 1: Below the test standard
Question 1
This literacy sample question is representative of the reading skills of candidates at Band 1: Below the
test standard. It requires candidates to locate directly stated information in a text with combinations of
written material and images, graphs or tables.
The question refers to the text Reading Success Test in the Appendix. 1
Which question appears to have been the most difficult for the students in this class?
Type the question number into the box below.
The question addresses the following aspects of the literacy assessment framework:
Literacy domain Reading
Text type Informative
Process Access and identify
Context Further education and professional learning
Indicative ACSF 2 Level 3
Relevant ACSF descriptor Understands familiar texts of limited complexity that may
incorporate graphs, tables and charts
Correct response 12
1
In the online test, stimulus text appears onscreen with each related question.
2
The Australian Core Skills Framework https://www.education.gov.au/australian-core-skills-framework
5
Question 2
This literacy sample question is representative of the technical skills of writing of candidates at Band
1: Below the test standard. Candidates are required to extend plans for writing (accurately place a new
idea into an existing structure of ideas).
The question refers to the text Homework in the Appendix.
All the information about the task needs to be put into the homework template.
Select the best heading from the homework template for each of the numbered sentences.
Learning Equipment The Submission
goals required task requirements
1. Get some thin cardboard from home
(cereal boxes are good) or the paper
recycling unit at school.
2. You will make three solid shapes out of
cardboard and sticky tape, with the
following volumes: 9, 24 and 154 cubic
centimetres.
3. You will apply your knowledge of
numbers, measurement and nets to construct
some solids.
4. Hand in your calculations, the net design
with the dimensions, and the three solids by
the end of next week.
The question addresses the following aspects of the literacy assessment framework:
Literacy domain Technical skills of writing
Technical skill of writing Text organisation
Context Schools and teaching
Indicative ACSF Level 4
Relevant ACSF descriptor Displays logical organisational structure in writing through the use of
coherently linked paragraphs
Equipment required, The task, Learning goals, Submission
Correct response
requirements
6Band 2: At and above the test standard
Question 3
This literacy sample question is representative of the reading skills of candidates at Band 2: At and
above the test standard. The question requires candidates to infer the position adopted by the writer of
the text.
The question refers to the text Letter From Hanoi in the Appendix.
The writer believes that the Christmas celebration is characterised by
A. angst and disharmony.
B. shallow entertainment.
C. making the most out of life.
D. a high regard for Vietnamese traditions.
The question addresses the following aspects of the literacy assessment framework:
Literacy domain Reading
Text type Descriptive
Process Integrate and interpret
Context Personal and community
Indicative ACSF Level 4
Relevant ACSF descriptor Understands texts incorporating some abstract ideas, symbolism and
embedded information, in which the relationship between concepts
and information is not explicit and requires inference and
interpretation
Correct response C
7Question 4
This literacy sample question is representative of the reading skills of candidates at Band 2: At and
above the test standard. The question requires the candidates to apply information in making
interpretations.
The question refers to the text Letter From Hanoi in the Appendix.
The writer appears to regard the children as
A. studious.
B. reserved.
C. resourceful.
D. accident-prone.
The question addresses the following aspects of the literacy assessment framework:
Literacy domain Reading
Text type Descriptive
Process Integrate and interpret
Context Personal and community
Indicative ACSF Level 4
Relevant ACSF descriptor Understands texts incorporating some abstract ideas, symbolism and
embedded information, in which the relationship between concepts
and information is not explicit and requires inference and
interpretation
Correct response C
8Question 5
This literacy sample question is representative of the technical skills of writing of candidates at Band
2: At and above the test standard. Candidates are required to correctly spell a polysyllabic word that is
frequently misspelt.
The sentence below contains one misspelt word.
Williams (2014) offers an elaborate and insightful analyses and critique of contemporary
pedagogical practice.
Type the word as it should appear.
The question addresses the following aspects of the literacy assessment framework:
Literacy domain Technical skills of writing
Technical skill of writing Spelling
Context Schools and teaching
Indicative ACSF Level 4
Relevant ACSF descriptor Accurately spells frequently used words, including relevant technical
terms and specialised vocabulary
Correct response analysis
9Question 6
This literacy sample question is representative of the technical skills of writing (punctuation) of
candidates at Band 2: At and above the test standard. Candidates are required to apply aspects of
punctuation that are frequently misused (apostrophes).
If the sentence below contains an error, correct the error by typing the word as it should appear
(type only one word); if there is no error, type N.
Respect everyones right to learn without interruption or disturbance.
The question addresses the following aspects of the literacy assessment framework:
Literacy domain Technical skills of writing
Technical skill of writing Syntax, Grammar and Punctuation
Context Schools and teaching
Indicative ACSF Level 3
Relevant ACSF descriptor Use punctuation as an aid to understanding, e.g. capitalisation, full
stops, commas, apostrophes, question marks and quotation marks
Correct response everyone’s
10Band 3: Clearly above the test standard
Question 7
This literacy sample question is representative of the reading skills of candidates at Band 3: Clearly
above the test standard. The question requires the candidates to evaluate the strategy adopted by the
writer of a text.
The question refers to the text Letter from Hanoi in the Appendix.
The writer expresses a feeling of conflict in paragraph 1.
The conflict is between
A. authority and caution.
B. tradition and flexibility.
C. tradition and superiority.
D. authority and irresponsibility.
The question addresses the following aspects of the literacy assessment framework:
Literacy domain Reading
Text type Descriptive
Process Evaluate and reflect
Context Personal and community
Indicative ACSF Level 4
Relevant ACSF descriptor Understands texts incorporating some abstract ideas, symbolism and
embedded information, in which the relationship between concepts
and information is not explicit and requires inference and
interpretation
Correct response B
11Question 8
This literacy sample question is representative of the reading skills of candidates at Band 3: Clearly
above the test standard. The question relates to a text that includes different text formats, and requires
the candidates to evaluate information from multiple parts of the text.
The question refers to the text Reading Success Test in the Appendix.
Are the statements listed below true or false for the Making Pies unit?
Select ‘True’ or ‘False’ for each statement.
Statement True False
The RI (Retrieving information) question is categorised as easier than
the IE (Interpreting explicit information) question.
The II (Interpreting by making inferences) question is categorised as
more difficult than the IE (Interpreting explicit information) question.
The RF (Reflecting on texts) question is the most difficult type of
question.
The question addresses the following aspects of the literacy assessment framework:
Literacy domain Reading
Text type Informative
Process Integrate and interpret
Context Further education and professional learning
Indicative ACSF Level 4
Relevant ACSF descriptor Understands texts incorporating some abstract ideas, symbolism and
embedded information, in which the relationship between concepts
and information is not explicit and requires inference and
interpretation
Correct response True, True, False
12Question 9
This literacy sample question is representative of the technical skills of writing (vocabulary) of
candidates at Band 3: Clearly above the test standard. Candidates are required to identify synonyms
for high-level words.
The underlined word in the sentence below is too difficult for the class’s rules.
Arbitrate difficulties with other classmates.
Select a synonym from the list below to replace it.
A. Report
B. Avoid
C. Agitate
D. Mediate
The question addresses the following aspects of the literacy assessment framework:
Literacy domain Technical skills of writing
Technical skill of writing Word usage
Context Schools and teaching
Indicative ACSF Level 5
Relevant ACSF descriptor Understands and uses appropriate specialised vocabulary in a variety
of situations, e.g. explanations, descriptions or arguments
Correct response D
13Described proficiency bands for numeracy
The following descriptions reflect the main content and processes that are assessed in the numeracy component of the test. For numeracy, the
content elements are number and algebra, measurement and geometry, and statistics and probability with a focus on number, measurement and
statistics. The process elements are identifying mathematical information and meaning in activities and texts; using and applying mathematical
knowledge and problem solving processes; and interpreting, evaluating, communicating and representing mathematics. An online calculator is
available for 80 per cent of the questions.
Table 3: Band descriptions for Number and Algebra
Number Band 1: Below the test standard Band 2: At and above the test standard Band 3: Clearly above the test standard
and
Algebra Candidates can typically Candidates can typically Candidates can typically
• use whole numbers and some common • demonstrate the skills described in Band 1 • demonstrate the skills described in Band 1 and
fractions, decimals and percentages • identify and use the appropriate operation (+, –, Band 2
1
(such as , 0.5, 10%) to solve one- or ×, ÷) and use proportional reasoning, and a • estimate and calculate accurately and use a
8
two-step routine problems, with or variety of fractions, decimals and percentages variety of less familiar fractions, decimals and
3 1
without a calculator (such as , 0.4, 85%) to solve multi-step percentages (such as , 9.93, 0.02%) to solve
5 16
• identify an appropriate formula (such as problems in familiar situations, with or without a problems set in less routine contexts, with or
how to calculate an average in a calculator without a calculator
spreadsheet) to solve problems in • use a formula in familiar contexts to calculate a • use a graphical representation of an algebraic
familiar contexts value relationship (such as a linear graph) to calculate a
value (such as a rate) in meaningful contexts
Skills required to transition from Band 1 to Band 2
• calculate with a wider variety of fractions, decimals and percentages
• solve problems of greater complexity (such as with more than two steps)
• understand and use the formulae in real-world contexts
Skills required to transition from Band 2 to Band 3
• calculate with a wider variety and less familiar fractions, decimals and percentages
• solve multi-step problems in less routine contexts
• understand and use representations of formulae in less routine contexts
14Table 4: Band descriptions for Measurement and Geometry
Measurement Band 1: Below the test standard Band 2: At and above the test standard Band 3: Clearly above the test standard
and
Geometry Candidates can typically Candidates can typically Candidates can typically
• interpret simple diagrams, read common • demonstrate the skills described in Band 1 • demonstrate the skills described in Band 1
scales, and use spatial skills such as • solve problems by applying knowledge and and Band 2
interpretation of simple maps to identify a understanding of measurement concepts such • link different information sources and apply
location or follow directions as the speed-distance-time relationship measurement knowledge and understanding
• use routine timetables and calendars to • apply spatial skills such as using scale to such as rates and area
calculate durations and identify times and find distance, and reorienting maps and plans • use spatial reasoning to interpret less routine
dates to determine directions and relative positions maps and diagrams, and solve multi-step
• interpret and use schedules and time displays problems
to determine durations and times, and to • interpret and use time-related criteria such as
solve problems schedules and regulations to solve multi-step
problems
Skills required to transition from Band 1 to Band 2
• understand and use rates and relationships (such as speed) to solve problems
• orient maps and use information such as scale to solve spatial problems
• use information on schedules and displays to accurately calculate durations
Skills required to transition from Band 2 to Band 3
• calculate area and volume using metric units in real-world contexts
• use ratio in relation to maps and plans to solve less routine spatial problems
• solve multi-step problems involving conversions between hours and minutes
15Table 5: Band descriptions for Statistics and Probability
Statistics Band 1: Below the test standard Band 2: At and above the test standard Band 3: Clearly above the test standard
and
Probability Candidates can typically Candidates can typically Candidates can typically
• interpret familiar data representations, • demonstrate the skills described in Band 1 • demonstrate the skills described in Band 1 and
evaluate some related statements and • interpret less familiar, relatively complex Band 2
solve routine problems using the data data representations (such as multi-category • interpret additional data representations and
• calculate everyday probabilities (such as graphs and tables), evaluate related diagrams (such as box-and-whisker plots and
20%) in familiar contexts statements and solve routine problems using Venn diagrams) and use them to identify key
the data aspects of the representations, evaluate related
• calculate and interpret small probabilities statements and solve more complex problems
(such as 0.3%) in meaningful contexts using the data
• interpret written text containing statistical
information and calculate a range of statistics
Skills required to transition from Band 1 to Band 2 (such as median and quartile)
• interpret a wider variety of more complex data displays and representations • calculate conditional probabilities in meaningful
contexts
• understand, use and calculate probability in a wider variety of situations
Skills required to transition from Band 2 to Band 3
• interpret more detailed statistical information and less routine data representations
• understand and use a wider range of statistics
• understand how probability can depend on given events and conditions
16Sample questions illustrating the numeracy band descriptions
Band 1: Below the test standard
Question 1
This numeracy sample question is representative of the geometric problem-solving skills of
candidates in Band 1: Below the test standard. The question requires candidates to see and use the
relationship between the paper sizes in the diagram provided. The question requires interpretation of
the diagram, some spatial reasoning and application of a counting strategy.
The diagram illustrates the relationship between an A0-size poster and other sizes.
What is the greatest number of A4-size posters that can be cut from an A0-size poster?
__________
Content domain Measurement and Geometry
Process domain Identifying mathematical information and meaning in activities and
texts
Context domain Personal and community
Calculator availability Available
Indicative ACSF Level 3
Relevant ACSF descriptor Interprets and comprehends familiar and routine length, mass,
volume/capacity, temperature and simple area measures
Correct response 16
17Question 2
This numeracy sample question is representative of the level of statistical interpretation and
identification required by candidates in Band 1: Below the test standard. The question requires
candidates to read and interpret a graphical representation of data. Reading between the marks on the
scale of each axis is not required and only identification of the curve passing through the point
corresponding to the given information is required.
This graph shows the length of boys from birth to 24 months by selected percentiles.
A boy is 74 cm long at 12 months.
His length is closest to which percentile?
A. 50th
B. 25th
C. 10th
D. 5th
18Content domain Statistics and Probability
Process domain Identifying mathematical information and meaning in activities and
texts
Context domain Personal and community
Calculator availability Available
Indicative ACSF Level 3
Relevant ACSF descriptor Selects and interprets mathematical information that may be partly
embedded in a range of familiar, and some less familiar, tasks and
texts
Correct response B
19Question 3
This numeracy sample question is representative of the proportional reasoning skills using fractions of
candidates at Band 1: Below the test standard. The question is set in a common everyday context and
a calculator is not available. Candidates who interpret the question correctly can use number sense to
rule out options A and B. It is likely that most candidates will be required to perform some calculation
to discriminate between options C and D. The essential understanding is to determine that five halves
is equivalent to two and a half.
A recipe for one batch of play dough is:
1 cup of salt
1
cup of water
2
1
1 cups of flour
2
2 tablespoons of cooking oil
food colouring
How many cups of flour are needed for 5 batches of play dough?
1
A. 3
2
1
B. 5
2
1
C. 6
2
1
D. 7
2
Content domain Number and Algebra
Process domain Using and applying mathematical knowledge and problem solving
processes
Context domain Personal and community
Calculator availability Not available
Indicative ACSF Level 3
Relevant ACSF descriptor Calculates with whole numbers and everyday or routine fractions,
decimals and percentages (includes dividing by small whole numbers
only)
Correct response D
20Band 2: At and above the test standard
Question 4
This numeracy sample question is representative of the statistical knowledge, reasoning and
interpretation skills of candidates in Band 2: At and above the test standard. For some candidates,
box-plots and dot-plots may be less familiar representations of data. For this type of multiple-choice
question, each of the statements must be interpreted correctly. The first two statements require
interpretation of one representation at a time. The third statement requires both representations to be
compared.
At a data interpretation workshop, teachers were given the following example.
In Year 7, a group of 29 students completed a reading test.
In Year 9, the same group of students completed a reading test from the same series.
The graphs below show their results.
Scores at Year 7 and Year 9 are reported on the same scale.
Below are some statements about the graphs.
Select ‘True’ or ‘False’ for each statement.
Statement True False
The difference between the highest and lowest Year 7 reading scores was 120.
Six Year 9 scores were greater than 585.
There is at least one student whose reading score has increased by 20 or more
from Year 7 to Year 9.
21Content domain Statistics and Probability
Process domain Interpreting, evaluating, communicating and representing mathematics
Context domain Further education and professional learning
Calculator availability Available
Indicative ACSF Level 4
Relevant ACSF descriptor Extracts, interprets and comprehends statistical data in complex tables
and spreadsheets, graphs, measures of central tendency, simple
measures of spread and common chance events
Correct response False, True, True
22Question 5
This numeracy sample question is representative of the algebra skills of candidates at Band 2: At and
above the test standard. While some candidates may find the spreadsheet context unfamiliar, it is
possible to use the information provided about spreadsheets to interpret the algebraic notation in the
options. A concrete strategy is to imagine three quantities, model the total cost calculation and then
determine which rule has the same structure as the calculation.
Mary’s Garden Supplies uses a spreadsheet to find the total cost of an order.
The quantity of each material ordered is entered into cells B2, B4 and B6.
The spreadsheet then calculates the total cost in cell B10.
Which formula can be used to find the total cost in cell B10?
A. =(B2*C2)+(B4*C4)+(B6*C6)
B. =(B2+C2)+(B4+C4)+(B6+C6)
C. =(B2*C2)*(B4*C4)*(B6*C6)
D. =(B2+B4+B6)*(C2+C4+C6)
23Content domain Number and Algebra
Process domain Interpreting, evaluating, communicating and representing mathematics
Context domain Personal and community
Calculator availability Available
Indicative ACSF Level 4
Relevant ACSF descriptor Uses a combination of informal, but mostly formal, written
mathematical and general language, including some specialised
mathematical symbolism, abbreviations, terminology and
representations to document, interpret and communicate
mathematically
Correct response A
24Question 6
This numeracy sample question is representative of the problem-solving skills of candidates at Band
2: At and above the test standard. It is a multi-step measurement problem that requires metric
conversion and formulation. The formulation involves the realisation that the length required is half
the difference between 3 metres and 120 centimetres. It also involves the realisation that the mixed
units requires conversion and the knowledge that one metre is equivalent to one hundred centimetres.
A teacher wants to place a map, with the dimensions shown, in the centre of a 3-metre wide display
board.
The two distances marked ‘length’ on the diagram are to be equal.
How many centimetres should each length be?
__________ cm
25Content domain Measurement and Geometry
Process domain Using and applying mathematical knowledge and problem solving
processes
Context domain Schools and teaching
Calculator availability Available
Indicative ACSF Level 3
Relevant ACSF descriptor Measures, estimates and calculates length, perimeter, mass,
capacity/volume, time, temperature and simple area (for rectangular
areas only) or estimates area of non-rectangular shapes
Correct response 90
26Question 7
This numeracy sample question is representative of the proportional reasoning skills of candidates at
Band 2: At and above the test standard. It also illustrates their ability to check the answer for
reasonableness within the given context. For example, in this case that a whole number response is
required. The type of information provided is in the form of an informal ratio and such statements are
common in educational and health and safety contexts. As such the context should be familiar to
almost all candidates. A calculator is not available for this question.
In one state of Australia, an Education Department regulation advises that two asthma emergency
kits should be provided for every 300 students, or part of 300 students.
A school has 530 students.
How many asthma emergency kits should be provided for the school?
__________
Content domain Number and Algebra
Process domain Using and applying mathematical knowledge and problem solving
processes
Context domain Schools and teaching
Calculator availability Not available
Indicative ACSF Level 3
Relevant ACSF descriptor Uses and applies rates in familiar or routine situations
Correct response 4
27Question 8
This numeracy sample question is representative of the spatial reasoning and map skills of candidates
in Band 2: At and above the test standard. For this type of multiple-choice question, each of the
statements must be interpreted correctly. Statements one and three require the ability to orientate
oneself on the map. The second statement requires use of the distance information on the map,
knowledge of metric conversion and estimation skills.
An online map shows this route from City Primary School to Steele Park, and related information.
Below are some statements about the map.
Select ‘True’ or ‘False’ for each statement.
Statement True False
When walking from City Primary School towards Steele Park along Grey St,
Bridge St is on the left.
The distance from the corner of Bridge St and Grey St to the entrance of
Steele Park is less than 200 metres.
The route from City Primary School to Steele Park requires three left turns
and one right turn.
28Content domain Measurement and Geometry
Process domain Interpreting, evaluating, communicating and representing mathematics
Context domain Personal and community
Calculator availability Available
Indicative ACSF Level 3
Relevant ACSF descriptor Uses a combination of both formal and informal symbolism, diagrams,
graphs and conventions relevant to the mathematical knowledge of the
level.
Correct response False, False, True
29Band 3: Clearly above the test standard
Question 9
This numeracy sample question is representative of the ability of candidates at Band 3: Clearly above
the test standard to interpret and use financial information provided in a table. In order to answer the
question correctly, the correct formulation must be selected using the information from multiple cells
in the table. It is also necessary to know that calculating 90% is equivalent to a 10% reduction.
A school is planning a 10-day Central Australia trip for 33 students and 3 teachers. This table
shows the charges and conditions.
10-day Central Australia Trip
Cost per student (35-40 students) $2750 per student (Full cost)
(30-34 students) $3200 per student (Full cost)
Early Bird rate (If paid in full 30 days before departure date) Save 10% of full cost
Deposit (Payable within 7 days of booking) 20% of full cost
Teachers (Up to 3 teachers) Free
Using the Early Bird rate, which of these shows how to calculate the total payable to the bus
company?
A. 10% of 33 × $3200
B. 10% of 36 × $2750
C. 90% of 33 × $2750
D. 90% of 33 × $3200
E. 90% of 36 × $2750
30Content domain Number and Algebra
Process domain Identifying mathematical information and meaning in activities and
texts
Context domain Schools and teaching
Calculator availability Available
Indicative ACSF Level 3
Relevant ACSF descriptor Selects and interprets mathematical information that may be partly
embedded in a range of familiar, and some less familiar, tasks and
texts
Correct response D
31Question 10
This numeracy sample question is representative of the level of personal numeracy of candidates at
Band 3: Clearly above the test standard. It is a multi-step problem for which a calculator is not
available. In order to provide a correct response, it is necessary to use the information in the table to
calculate a duration in minutes, subtract the time intervals in the information provided below the table,
and divide the remaining time by the number of games.
A games afternoon is organised at a school.
The students are divided into four groups: red, blue, green and yellow.
Each group rotates through four games as shown in the table.
Red Blue Green Yellow
Start 1:30 pm Game 1 Game 2 Game 3 Game 4
Break
Game 2 Game 3 Game 4 Game 1
Break
Game 3 Game 4 Game 1 Game 2
Break
Game 4 Game 1 Game 2 Game 3
Presentations
End 3:15 pm
There is a 5-minute break between each game and 10 minutes are allocated for presentations.
How many minutes are allocated for each game?
_________ minutes
32Content domain Measurement and Geometry
Process domain Using and applying mathematical knowledge and problem solving
processes
Context domain Schools and teaching
Calculator availability Not available
Indicative ACSF Level 3
Relevant ACSF descriptor Measures, estimates and calculates length, perimeter, mass,
capacity/volume, time, temperature and simple area. Selects from and
uses a variety of developing mathematical and problem solving
strategies in a range of familiar and some less familiar contexts
Correct response 20
33Question 11
This numeracy sample question is representative of the statistical knowledge and understanding of
candidates at Band 3: Clearly above the test standard. It is the second question relating to the same
text as sample question 4 in Band 2. For some candidates, box-plots and dot-plots may be less familiar
representations of data. In order to provide a correct response, two strategies are possible. One is to
use each dot-plot to determine each middle value. The other is to use the median line in each box-plot
to read each median off the scale. The last step is to subtract the median values to find the difference.
At a data interpretation workshop, teachers were given the following example.
In Year 7, a group of 29 students completed a reading test.
In Year 9, the same group of students completed a reading test from the same series.
The graphs below show their results.
Scores at Year 7 and Year 9 are reported on the same scale.
What is the difference between the median (middle) reading scores of Year 7 and Year 9?
__________
34Content domain Statistics and Probability
Process domain Identifying mathematical information and meaning in activities and
texts
Context domain Further education and professional learning
Calculator availability Available
Indicative ACSF Level 4
Relevant ACSF descriptor Extracts, interprets and comprehends statistical data in complex tables
and spreadsheets, graphs, measures of central tendency, simple
measures of spread and common chance events
Correct response 15
35Question 12
This numeracy sample question is representative of the understanding of probability of candidates in
Band 3: Clearly above the test standard. In order to provide a correct response, it is necessary to
realise that the probability is dependent upon the given condition, that a girl is selected. The fraction
obtained must then be expressed as a percentage.
Two Year 5 students, one girl and one boy, are to be randomly selected to read at an assembly.
There are two Year 5 classes, 5A and 5B.
The girls’ names and the boys’ names are placed into separate containers.
The numbers of girls and the numbers of boys from each class are shown.
A girl is selected.
What is the chance that the selected girl is from class 5A?
Express your answer as a percentage.
__________ %
Content domain Statistics and Probability
Process domain Using and applying mathematical knowledge and problem solving
processes
Context domain Schools and teaching
Calculator availability Available
Indicative ACSF Level 4
Relevant ACSF descriptor Uses knowledge about chance and probability to estimate and interpret
the outcomes of common chance events in both numerical and
qualitative terms
Correct response 40
36Appendix
Reading Success Test
A teacher has administered a Reading Success Comprehension Test to her class.
Section 1 below is an extract from the printed report of the results from the class. Section 2 is a list of
terms relating to the extract.
SECTION 1
SECTION 2
An explanation of terms from the Reading Success Comprehension Test report
371. Question Difficulty. Higher numbers indicate more challenging questions based on responses
from 2000 students in a norm study.
2. Question Type. Questions are categorised into areas of reading comprehension: IE (Interpreting
explicit information), II (Interpreting by making inferences), RF (Reflecting on texts) and RI
(Retrieving information).
3. Correct Answers. The correct answer (a letter response: A, B, C or D) is given immediately
below the Question Number for each question.
4. Students’ Responses. The spreadsheet indicates each student’s response. Incorrect responses are
shaded light grey. Missing answers, where students did not give any response, are marked with an
M and shaded dark grey.
38Homework
This is a draft text for a homework task.
In this task you will be using your maths skills to make a shape.
1. Get some thin cardboard from home (cereal boxes are good) or the paper recycling unit at school.
2. You will make three solid shapes out of cardboard and sticky tape, with the following volumes: 9,
24 and 154 cubic centimetres.
3. You will apply your knowledge of numbers, measurement and nets to construct some solids.
4. Hand in your calculations, the net design with the dimensions, and the three solids by the end of
next week.
5. Put everything together in a sealed, named bag.
6. Make sure you have scissors, sticky tape and cardboard to make your shapes.
39Letter From Hanoi
This is a personal letter from the Australian International Academic Director of a large bilingual
school in Hanoi, Vietnam.
Today was our Christmas celebration at school, ending the term with a two-week gap before the
students commence their Term 3 studies. Christmas is not a traditional celebration for the Vietnamese,
yet they embrace it wholeheartedly. Many of the students turn up in Santa suits themselves. I find
myself wanting to say, ‘This is all wrong,’ as though I have some superior right or knowledge to
dictate how Christmas ought to be celebrated.
We help our Santa (a burly New Zealand teacher) to get ready in the office. The Vietnamese Santa
suit is a very flimsy affair and we use several safety pins and extra cotton wool to beef up the whole
effect. It’s a tight squeeze in the Asian-sized suit but he doesn’t worry too much about showing a bit
of ankle and wrist. Santa and the science teacher, a six-foot-tall Irish elf dressed entirely in green and
armed with a lolly bag, set off around the school on a motorbike, beeping madly so the students will
come to the windows. The teachers are excited and encourage the children to chase the bike. Santa
and the elf are afraid to stop, followed as they are by a mob of about 400 running, squealing children.
My mind is reeling with the health and safety implications of wholesale, lawless chaos.
I shouldn’t really have worried. Here the children kick a ball on the roof and calmly go and borrow a
ladder from the janitor or climb out a window to retrieve it, much to my Westerner’s anguish. To my
knowledge, there has been no ambulance summons or serious injury in the two years I’ve been here.
Order is eventually restored and Santa and his elf dismount from their bike to visit each classroom,
distribute candy and have photos taken. The children seem a little confused about asking for presents
from this man called Santa. They usually receive ‘lucky money’ at Lunar New Year or on their
birthdays, but all the same they are happy to go along with the big ‘Ho-ho-ho-ing’ guy in the red suit
who says he's going to visit their house quite soon.
The only glitch in the day really comes when the preschool teachers insist Santa wake the
kindergarteners from their lunchtime sleep. I desperately want to intervene, but restrain myself.
Predictably, there are tears and howls of terror from four-year-olds woken from a peaceful snooze by
a massive, bearded stranger leaning over their cots. Santa and his elf are definitely traumatised by the
whole event. The staff giggle and shhhhh, beaming tolerantly as they usher their sobbing charges into
position for the inevitable group photograph. Later in the day, these children are exultant about their
tearful Santa photo. My overprotective Western thinking has been challenged yet again.
There is a performance in the afternoon. Christmas songs are performed with gusto, not only by the
children, but by the Vietnamese teachers of each sector of the school, who dress up in cute, specially
made red and white costumes and compete vigorously with each other for cash prizes. Our
international teachers slink away to the back of the crowd; I wish they could let go of their cultural
inhibitions and get more involved.
Singing is big here. I was invited to sing at the opening of the first board meeting of the school year
where we sipped red wine at 10 am and ate fruit to celebrate. Not wanting to offend, I reluctantly
responded with a rather shaky, unaccompanied rendition of ‘You are my sunshine’ to serious-faced
executives who solemnly clapped and nodded their appreciation.
For this Christmas occasion I am required to make a speech, which is translated by the young assistant
at my side. It doesn’t matter really: no one is listening; no one ever does listen to speeches from
anybody. It is the formality that is important. The audience talk and call out to each other throughout
40and the speakers speak on regardless. It took me a while to understand this. A Vietnamese explained
to me once: ‘We Vietnamese are very good at multi-tasking.’
The elf delivers a fine performance of ‘Jingle bells’ to uproarious applause. I think again, as I have so
many times before, how lucky I am to share the sheer fun that the Vietnamese seem to wring out of
every occasion.
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